<p>In the field of liquid sloshing, the investigations based on potential flow theory have predominantly focused on linear or nonlinear models in unbaffled liquid tanks, cylindrical tanks with baffles, and rectangular tanks with horizontal baffles. However, there is a notable lack of systematic theoretical investigations into the specific influence of rigid vertical baffles in rectangular liquid tanks on nonlinear sloshing dynamics, particularly concerning complex dynamic characteristics and potential chaotic phenomena under nonlinear conditions. This study addresses this gap by integrating the Multi-Domain Eigenvalue Matching (MDEM) method with multi-dimensional modal theory to systematically analyze the nonlinear effects of vertical baffles on liquid sloshing. The analytical form of potential functions in different regions is first derived using the MDEM method. Through the modal superposition method, these potential functions and wave height functions are expressed as Fourier series incorporating generalized coordinate time. A finite-dimensional modal system equation is then established by applying the Bateman-Luke variational principle and Moiseev asymptotic approximation. The damping coefficient is experimentally determined, and the theoretical solutions demonstrate strong agreement with experimental data in terms of wave height and dynamic pressure. The study investigates the influence of vertical baffles on nonlinear liquid sloshing under both free sloshing and lateral excitation conditions. The results reveal that higher baffle positions lead to stronger wave reflections, driving the transition from linear to nonlinear sloshing regimes. This transition is characterized by increasingly chaotic trajectories and more complex waveform patterns.</p>